Relational order theories

A number of independent lines of research depict the universe, including the social organization of living creatures which is of particular interest to humans, as systems, or networks, of relationships.

Relational systems, or regimes, are often seen as differentiated -- and thus defined -- by reductions in degrees of freedom among the elements of the system. This diminution in degrees of freedom in relationships among elements is characterized as correlation. The correlation process is sometimes seen as tiered through several levels, reaching from quantum mechanics upward through complex, dynamic, ‘non-equilibrium’, systems, including living systems.

The quantum mechanics level

Lee Smolin [ ‘The Life of the Cosmos’, Lee Smolin, Oxford University Press, 1997 ] proposes a system of "knots and networks” such that "the geometry of space arises out of a … fundamental quantum level which is made up of an interwoven network of … processes”. [Smolin, supra. p. 283] Smolin and a group of like minded researchers have devoted a number of years to developing a loop quantum gravity basis for physics, which encompasses this relational network viewpoint.

Carlo Rovelli and associated persons have, in parallel and in communication with Smolin and associates, begun to elaborate a system called Relational quantum mechanics, which has at its foundation the view that all systems are quantum systems, and that each quantum system is defined by its relationship with other quantum systems with which it interacts. Rovelli has proposed that each interaction between quantum systems involves a ‘measurement’, and such interactions involved reductions in degrees of freedom between the respective systems, to which he applies the term correlation.

These lines of inquiry are developed at more length by the authors and other investigators, and in the linked pages in this encyclopedia. The linked pages are more technical and detailed in nature than this very summary reflection of some of the central elements.

Though the proponents of these theories seem confident that they are on the right track, they are candid in reflecting that their work requires considerable investigation and elaboration in competition with and integration with other perspectives on quantum mechanics, Einsteinian relativity, string, and other fundamental theories of physics.

The cosmological level

The conventional explanations of big bang and related cosmologies (see also Timeline of the Big Bang) projects an expansion of and related ‘cooling’ of the universe which entails a cascade of phase transitions involving fundamental forces, quark-gluon transitions to simple atoms, complex atoms, simple and complex molecules, and aggregations of these entities into galaxies, stars, planets, etc. (Strictly speaking, phase transitions can both manifest correlation and differentiation events, in the direction of diminution of degrees of freedom, and in the opposite direction disruption of correlations. However, the expanding universe picture presents a framework in which there appears to be a direction of phase transitions toward differentiation and correlation, in the universe as a whole, over time) At least at the level of aggregation of baryons, each correlated and differentiated system thus evolved can be considered, from the relational point of view, as a network of relationships.

David Layzer [Cosmogenesis: The Growth of Order in the Universe, by David Layzer, Oxford Univ. Press, 1991] and Eric Chaisson [ Chaisson, “Cosmic Evolution”, Harvard, 2001 ] have provided slightly varying but compatible explanations of how the expansion of the universe allows ordered, or correlated, relational regimes to arise and persist, notwithstanding the second law of thermodynamics.

Layzer spoke in terms of the rate of expansion outrunning the rate of equilibration involved at local scales, while Chaisson summarizes the argument as “In an expanding universe actual entropy … increases less than the maximum possible entropy“ [Chaisson, id p. 130] thus allowing for, or requiring, ordered (negentropic) relationships to arise and persist.

Chaisson depicts the universe as a non-equilibrium process, at least in this sense, in which energy flows into and through ordered systems, such a galaxies, stars, and life processes. This provides a cosmological basis for non-equilibrium thermodynamics, treated elsewhere to some extent in this encyclopedia at this time. In terms which unite non-equilibrium thermodynamics language and relational analyses, patterns of processes arise and are evident as ordered, dynamic relational regimes.

Life Organization Level

Basic levels

There seems to be agreement that life is a manifestation of non-equilibrium thermodynamics, both as to individual living creatures and as to aggregates of such creatures, or ecosystems. See e.g. Brooks and Wylie [ “Evolution as Entropy”, Brooks and Wylie, University of Chicago press, p 103 et seq ] Smolin, [Smolin, Ch. 11 “What is Life”] Chaisson, Stuart Kauffman [ "Investigations", Stuart Kauffman, Oxford Univ Press, 2000 and "Origins of Order", Oxford, 1993] and Ulanowicz. [ "Ecology, the Ascendent Prespective”, Robert Ulanowicz, Columbia Univ. Press 1997 ]

This realization has proceeded from, among other sources, a seminal concept of ‘dissipative systems’ offered by Ilya Prigogine. In such systems, energy feeds through a stable, or correlated, set of dynamic processes, both engendering the system and maintaining the stability of the ordered, dynamic relational regime.

In the 1990s, Eric Schnieder and J.J. Kaye [ Schneider, E. D., and J. J. Kay. 1994. Complexity and Thermodynamics: Towards a New Ecology. Futures 26: 626–647.] began to develop the concept of life working off differentials, or gradients (e.g. the energy gradient manifested on Earth as a result of sunlight impinging on earth on the one hand and the temperature of interstellar space on the other). Schneider and Kaye identified the contributions of by Prigogine and Erwin Schrödinger What is Life? (Schrödinger) as foundations for their conceptual developments.

Schneider and Dorion Sagan have since elaborated on the view of life dynamics and the ecosystem in “Into the Cool “. [ “Into the Cool” , Schneider and Sagan, University of Chicago, 2005)] In this perspective, energy flows tapped from gradients create dynamically ordered structures, or relational regimes, in pre-life precursor systems and in living systems.

As noted above, Chaisson [Chaisson, supra p. 223-224] has provided a conceptual grounding for the existence of the differentials, or gradients, off which, in the view of Kaye, Schneider, Sagan and others, life works. Those differentials and gradients arise in the ordered structures (such as suns, chemical systems, and the like) created by in correlation processes entailed in the expansion and cooling processes of the universe.

Two investigators, Robert Ulanowicz [ "Ecology, the Ascendent Prespective”, Robert Ulanowicz, Columbia Univ. Press 1997 ] and Stuart Kauffman, . [Kauffman, supra] have suggested the relevance of autocatalysis models for life processes. In this construct, a group of elements catalyse reactions in a cyclical, or topologically circular, fashion.

Several investigators have used these insights to suggest essential elements of a definition of the life process, which might briefly be summarized as stable, patterned (correlated) processes which intake (and dissipate) energy, and reproduce themselves. [ See Brooks and Wylie, Smolin, Kauffman, supra, and Pearce [http://www.pearcesite.net/docs/pws-lifefundchap1105.doc] ]

Ulanowicz, a theoretical ecologist, has extended the relational analysis of life processes to ecosystems, using information theory tools. In this approach, an ecosystem is a system of networks of relationships (a common viewpoint at present), which can be quantified and depicted at a basic level in terms of the degrees of order or organization manifested in the systems.

Two prominent investigators, Lynn Margulis and, more fully, Leo Buss [“The Evolution of Individuality”, Leo buss, Princeton Univ. Press, 1997 ] have developed a view of the evolved life structure as exhibiting tiered levels of (dynamic) aggregation of life units. In each level of aggregation, the component elements have mutually beneficial, or complementary, relationships.

In brief summary, the comprehensive Buss approach is cast in terms of replicating precursors which became inclusions in single celled organisms, thence single celled organisms, thence the eukaryotic cell (which are, in Margulis’ now widely adopted analysis, made up of single celled organisms), thence multicellular organisms, composed of eukaryotic cells, and thence social organizations composed of multicellular organisms. This work adds to the ‘tree of life’ metaphor a sort of ‘layer cake of life’ metaphor., taking into account tiered levels of life organization.

Social organization

Social network theory has in recent decades expanded into a large field reaching across a large range of topics. Among other things, social network analyses are now applied to political, professional, military, and other closely attended subject matters. See e.g. the explanation, references and links in the Social Network article in this encyclopedia.

The internet, because of its low cost, broad reach, and combinatorial capacity, has become a prominent example of social networking, as is evident in this encyclopedia, Youtube, Facebook, and other recent developments. As a readily available illustration of a dynamic relational network system, at the human technology level, the internet has become a subject for analyses of how networks of relationships can arise and function.

Related areas of current interest

Second law of thermodynamics

The development of non equilibrium thermodynamics and the observations of cosmological generation of ordered systems, identified above, have engendered proposed modifications in the interpretation of the Second Law of Thermodynamics, as compared with the earlier interpretations on the late 19th and the 20th century. For example, Chaisson and Layzer have advanced reconciliations of the concept of entropy with the cosmological creation of order. In another approach, Schneider and D. Sagan, in “Into the Cool’ and other publications, depict the organization of life, and some other phenomena such as benard cells, as entropy generating phenomena which facilitate the dissipation, or reduction, of gradients (without in this treatment visibly getting to the prior issue of how gradients have arisen.).

The ubiquity of ‘power law’ and log normal distribution manifestations in the Universe

The development of network theories has yielded observations of widespread, or ubiquitous, appearance of ‘power law’ and ‘log normal’ distributions of events in such networks, and in nature generally. (Mathematicians often distinguish between ‘power laws’ and ‘log normal’ distributions, but not all discussions do so.) Two observers have provided documentation of these phenomena, Albert-Laslo Barabasi, [ "Linked”, Barabasi, Perseus Press, 2002 ] , and Mark Buchanan [ “Ubiquity”, Mark Buchanan, Three Rivers Press, 2002. See also “Nexus”, Buchanan, Norton & Co., 2002 ]

Buchanan demonstrated that power law distribution occur throughout nature, in events such as earthquake frequencies, the size of cities, the size of sun and planetary masses, etc. Both Buchanan and Barabasi reported the demonstrations of a variety of investigators that such power law distributions arise in phase transitions.

In Barabasi’s characterization “…if the system is forced to undergo a phase transition … then power laws emerge – nature’s unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self organization and paved with power laws.”. [, Barabasi, supra, p.77 ]

Given Barabasi’s observation that phase transitions are, in one direction, correlational events yielding ordered relationships, relational theories of order following this logic would consider the ubiquity of power laws to be a reflection of the ubiquity of combinatorial process of correlation, expressed in phase transitions. .

Emergence

There has been considerable comment on the concept of ‘emergence’ in recent decades. See Emergence This summary of relational regime theories will not create a detailed analysis or a summary of literature, as this might be done elsewhere. However, one can note and briefly illustrate that the relational regime approach includes a straightforward derivation of the concept of emergence.

That is, from the perspective of relational theories of order, emergent phenomena could be said to be relational effects or characteristics of an aggregated and differentiated system made of many elements, in a field of relationships external to the considered system, when the elements of the considered system, taken alone, would not have such an effect.

For example, the stable structure of a rock, which allows very few degrees of freedom for its elements, can be seen to have a variety of external manifestations depending on the relational system in which it may be involved. It could impede fluid flow, given some conditions. In a regime of gases, it will exclude most components of the gas from the space it occupies, ( or incorporate some of them, depending on its structure). In contests among rivalrous humans, it has sometimes been a convenient skull cracker. Or it might become a composite element of another solid, with similarly reduced degrees of freedom for its components, as would a pebble in a matrix making up cement.

To shift particulars, embedding carbon filaments in a resin making up a composite material can yield ‘emergent’ effects. (See the composite material article for a useful description of how varying components can, in a composite, yield effects within a field of use which the components alone would not yield).

That this derivation of the concept of emergence is conceptually straightforward and this brief reflection of this derivation uses simple illustrations does not imply that the relational system may not itself be complex, or participate as an element in a complex system of relationships – as is illustrated using different terminology in some aspects of the linked emergence and complexity articles..

The Arrow of time

As the article on the Arrow of time in this encyclopedia makes clear, there have been a variety of approaches to defining time and defining how time may have a direction.

The theories which outline a development of order in the universe, rooted in the asymmetric processes of expansion and cooling, project an ‘arrow of time’ – i.e. a sustained process which as it proceeds yields changes of state which do not appear, in the aggregate, to be reversible, over the universe as a whole.

Given the challenges confronting humans in determining how the Universe may evolve over billions and trillions of our years, it is difficult to say how long this arrow may be and the eventual end state it targets. At this time some prominent investigators suggest that much if not most of the visible matter of the universe will collapse into black holes which can be depicted as isolated, in a static cosmology. [ "The Return of a Static Universe and the End of Cosmology", Krauss, Lawrence, and Scherer, Robert, Journal of General Relativity and Gravitation, Vol 39, No. 10, pp. 1545-1550, October 2007. See also "The End of Cosmology", Scientific American, March 2008 for additional references. ]

Economics

Albert-Laslo Barabasi, Igor Matutinovic [ I. Matutinovic, 2005. The Microeconomic Foundations of Business Cycles: From Institutions to Autocatalytic Networks. Journal of Economic Issues, Vol 39, No.4., 867-898; I. Matutinovic, 2006. Self-Organization and Design in Market Economies. Journal of Economic Issues, Vol XL, No.3, 575-601.] and others have suggested that economic systems can fruitfully be seen as network phenomena generated by non-equilibrium forces.

At this time there is a visible attempt to re-cast the foundations of the economics discipline in the terms of non-equilibrium dynamics and network effects, led by researchers belonging to the school of evolutionary and institutional economics (Jason Potts), and ecological economics (Faber et al.). [ Faber Malte, Reiner Manstetten, and John Proops, 1998. Ecological Economics: Concept and Methods. Edward Elgar.]

Outside this group, some economists have adopted the language of ‘network industries’.The Economics of Network Industries, Oz Shy, University of Haifa, Israel, 2001, and Competition Policy In Network Industries: An Introduction, paper 0407006 by Nicholos Economides, New York University, a part of a series on industrial organization. ]

However, at this time there is not widespread treatment of this approach in the traditional mainstream economic journals. Given the well developed academic traditions of the economic discipline and the explanatory power of current approaches to economic phenomena, further developments along this line may take some time to evolve.

See also

* autocatalysis
*Autocatalytic set
* Emergence
* Dissipative systems
* Ecosystem
* phase
* phase transition
* Self-organization
* Self-organized criticality
* System
* Systems theory

References